Simplify (4^2*4^3)÷(4^-4)

$4^{2} \cdot 4^{3} \div 4^{- 4}$

Step 1

Rewrite the division as a fraction.

$\frac{4^{2} \cdot 4^{3}}{4^{- 4}}$

Step 2

Multiply $4^{2}$ by $4^{3}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4^{2 + 3}}{4^{- 4}}$

Add $2$ and $3$ .

$\frac{4^{5}}{4^{- 4}}$

Step 3

Move $4^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4^{5} \cdot 4^{4}$

Step 4

Multiply $4^{5}$ by $4^{4}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4^{5 + 4}$

Add $5$ and $4$ .

$4^{9}$

Step 5

Raise $4$ to the power of $9$ .

$262144$